wave question phy plz help?

2016-04-17 12:47 pm

17. A small boat ﬂoats on the sea. It encounters waves of the form y(x,t) = Asin(kx−ωt) where y(x,t) is the height of the wave at position x and time t, and k and ω are constants. The waves have a wavelength of 10 metres, amplitude of 0.5 metres, and travel at a horizontal speed of 2 metres per second. What is the maximum vertical velocity of the boat?

回答 (1)

天同

2016-04-18 4:49 am

✔ 最佳答案

Angular frequency ω = 2.(pi)f = 2.(pi).(v/入)
where f is the (linear) frequency, v is the speed of wave, 入 is the wavelength of the wave, and (pi) = 3.14159....
Hence, ω = 2.(pi).(2/10) s^-1 = 2(pi)/5 s^-1

As the waves pass through, the boat undergoes Simple Harmonic Motion (SHM) with an angular frequency ω of 2(pi)/5 s^-1

The velocity v of an object undergoing SHM is given by,
v = ω.[square-root(A^2 - y^2)]
where A is the wave amplitude and y is the displacement about the mean position.

The maximum velocity occurs when y = 0
Thus, maximum velocity =ωA = [2(pi)/5].(0.5) m/s = 0.628 m/s

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